A Fast Computer Aided Design Method for Filters

Transcription

1 2017 Asa-Pacfc Engneerng and Technology Conference (APETC 2017) ISBN: A Fast Computer Aded Desgn Method for Flters Gang L ABSTRACT *Ths paper presents a fast computer aded desgn method for flters based on model correcton technque. Through the smulaton of the submodels, the fttng formulas between the structure szes and the coeffcents can be determned. By pre-approved fttng formulas, the teratve correcton s carred out on the flter structure szes untl the performance meets the specfcaton. A desgn example s provded to explan the whole procedures. Smulaton results agree well wth the theoretcal synthess results whch confrm the valdty of the proposed method. INTRODUCTION The classcal mcrowave flter desgn method usually ncludes three procedures. Frst, the couplng matrx s obtaned accordng to the flter specfcaton [1,2]. Second, t s to determne the ntal structural dmensons of the flter based on the Egen mode method and the reflecton delay method [3,4]. Last, the optmsaton by full wave smulaton s always needed to make the flter response meet the specfcaton. The full wave optmzaton of the flter s tme-consumng and the results are not easy to converge. The space mappng algorthm [5,6], has been wdely used n the desgn of mcrowave passve devces n recent years. In ths method, the tme-consumng full wave smulaton optmzaton s transferred to the model optmzaton of rough space. Because of the short tme of model optmzaton n rough space, the optmzaton tme s remarkably shortened. However, because of the nonlnear mappng relatonshp between rough space and fne space and the unqueness of the parameter extracton results, the method s not effectve n the desgn of complex structures [7,8]. Ths paper presents a fast computer aded method for flters based on model correcton technque. After the couplng coeffcents of the flter are extracted by the admttance matrx Y parameters, the nformaton of the flter structure sze s obtaned by teratve correcton process. The teratve process s contnued untl flter response meets the specfcaton and fnally the structure szes of flter are determned. Gang L * School of Physcs and Electronc Engneerng, Hube Unversty of Arts and Scence, , Xang Yang, Chna Correspondng author: anson_lgang@163.com 1782

2 FUNDAMENTAL THEORY Couplng Coeffcent Extracton Accordng to the crcut theory, the admttance matrx Y parameters of a recprocal passve network wth two ports are as follows: y11 y12 [U] [I] (1) y12 y 22 Fgure 1 shows the equvalent crcut. y 12 y 11 y12 y22 y12 Fgure 1. Equvalent crcut of the admttance matrx. The crcut model n Fgure 1 s deformed nto the model n Fgure 2. The ABCD parameters of the three components marked by the dotted lne are determned as follows: Fgure 2. Equvalent crcut deformaton. 0 1 y12 [ ABCD] y12 0 (2) If the elements n the network are reactve elements, t s easy to obtan the followng relatonshp: 1 0 j [ ABCD] J (3) j J 0 Formula (3) mples the nverter model wth the characterstc admttance J. From the above deducton, t s concluded that the network marked by dotted lne n Fgure 2 can be equvalent to an nverter wth the characterstc admttance J. The dervaton process s ndependent of frequency and can be appled to all frequences. It s straghtforward to extend the model of Fgure 2 to the model of Fgure 3. y ( f ) 11 J Im ag( y ) y ( f ) Fgure 3. General admttance parameter equvalent crcut. The admttance on both sdes of the two port network s a functon of frequency. The model of Fgure 3 can correspond to a two resonant cavty model. Accordng to the defnton of the couplng coeffcent of the couplng cavty: 1783

3 k J (4) BB j The parameters n formula (4) can be represented by the admttance Y parameter and the formula of the couplng coeffcent s ntroduced: mag( y, j) (5) k y y jj f f Further, accordng to the physcal meanng of the admttance Y parameter, f the resonant cavty s resonant, the magnary part of the correspondng admttance Y parameter s equal to 0. So, the expressons of the resonant frequency of the cavty can be obtaned: f0 rootsmag( y) 0 (6) So far, we have deduced the formula of couplng coeffcent and resonant cavty frequency wth admttance Y parameters of crcut. From the above formulas, as long as admttance Y parameter s known, we can calculate the couplng coeffcent and resonant frequency at one tme. The above method apples not only to the two resonant cavty stuaton, also sutable for mult- resonant cavty stuaton. Model Correcton Technque After applyng the admttance Y parameter method to obtan the couplng coeffcent and the resonant frequency of the flter, the most mportant problem s now to determne the structure sze of the flter. Frstly, the relatonshp between the resonant frequency of sngle cavty and the tunng screw s smulated by smulaton software. The relatonshp between the couplng coeffcent of the cavty and the nserton depth of the couplng screw s calculated by usng the double cavty Egen mode method. After gettng the fttng functon relaton, the theoretcal value of each cavty s obtaned by the value of the matrx synthess theory. Accordng to the above theoretcal dmensons, the full wave model of the flter s establshed, and the smulaton of the whole cavty s carred out. The couplng coeffcent and the resonant frequency nformaton are extracted by the admttance Y parameter method. Because the cavty n the smulaton, the mutual nfluence of the cavty, the extracton value of the couplng coeffcent of resonant frequency s not exactly same wth the theoretcal value. Then, the dfference s determned by the formula (7): ( k) * ( k1) d d d (7) ( k) * ( k1) d d d Then, the structure sze s modfed accordng to the formula (8): d d d d d d ( k) ( k1) ( k) ( k) ( k1) ( k) j (0) * (0) * Where d d and d d. The teratve process s contnued untlflter response meets the specs. (8) 1784

4 EXAMPLE A fourth-degree Chebyshev flter wth 21-dB return loss s demonstrated as an example. The center frequency f s 1 GHz and the FBW s 2.19%. 0 Frstly, the couplng coeffcents are obtaned: M12=M34=0.0205, M23= The Q value s to All resonant frequences are equal to 1 GHz. These parameters are the optmal theoretcal values of rough space. Because of the symmetrcal structure of the flter, there are 5 parameters that need to be adjusted, whch are shown n Fgure 4. Fgure 4. Schematc dagram of flter. Fgure 5 shows the ntal response of the flter, and compares the response obtaned by the HFSS smulaton and the smulaton results obtaned by the Y parameter extracton method. It can be seen from the graph that the two are n good agreement, ndcatng that the Y parameter method s accurate for the parameter extracton, but the response of the flter detunes badly. Fgure 5. Flter responses of the matrces. Fgure 6. Flter responses of the matrces. Fgure 6 shows the fnal response of the flter sze and the theoretcal desgn response after the 4 teratons. It can be seen that the flter response s very close to the response of the theoretcal model. The szes of the flter durng teraton are shown n Table 1. Table 1. Structure szes of the flter durng teraton (mm). H1 C1 C t 2 1 t CONCLUSION The desgn effcency of the flter s mproved by combnng the couplng coeffcent extracton method of the equvalent crcut Y parameters and the model 1785

5 correcton technque. An example of a 4 cavty coaxal flter s used to verfy the correctness and effectveness of the proposed method. Ths method can also be appled to the desgn of other knds of flters, such as cross coupled resonator flters and so on. Ths work s supported by the Scence and Technology Research Project of Department of Educaton of Hube Provnce under project No.Q REFERENCES [1] R.J. Cameron, IEEE Trans. Mcrowave Theory Tech., 51, (2003). [2] W. Meng and K.L. Wu, IEEE Trans. Mcrowave Theory Tech., 54, (2006). [3] R.J. Cameron, C. Kudsa, and R. Mansour, Wley, (2007) [4] W. Meng, IEEE Trans. Mcrowave Theory Tech., 59, (2013). [5] S. Kozel and J.W. Bandler, IEEE Trans. Mcrowave Theory Tech., 55, (2007). [6] L. Szydlowsk, A. Lameck, and M. Mrozowsk, IEEE Mcrow. Wreless Compon. Lett., 22, (2012). [7] S. Kozel and J.W. Bandler, IEEE Trans. Mcrowave Theory Tech., 56, (2008) [8] S. Amar, M. Bekhet, and F. Seyfert, IEEE MTT-S Int. Mcrowave Symp. Dg., (2008). 1786